Answer:
(x, y) ⇒ (-x, y)
Step-by-step explanation:
Any transformation that multiplies a variable by something other than ±1 is not a rigid transformation — it involves some sort of dilation. Constants can be added or subtracted to effect translation, but none of the transformations shown here do any translation.
The first transformation is a reflection across the y-axis, hence the rigid transformation you're looking for.
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Comment on rotations
A rotation about the origin can be written in the form ...
(x, y) ⇒ (ax -by, bx +ay)
where a^2 +b^2 = 1 and b/a = tan(angle of rotation)
This rigid transformation is an exception to the statement above about multiplication by something other than ±1.
